[en] A review of the present status of quantum electrodynamics (QED) of strong fields is given with an emphasize on the special case of the Coulomb field (Z> or approximately Zsub(cr), where Zsub(cr) approximately 170 is the critical values of nuclear charge at which the electron ground state reaches the boundary of the lower continuum). The physics of phenomena in the overcritical region is considered, ereqg. vacuum polarization rearrangement at Z=Zsub(cr), spontaneous position production by the Coulomb field and the properties of the electron shell of an overcritical atom. The possibility to observe spontaneous and induced positron production in heavy ion collisions and the significance of these experiments for QED tests is discussed

[en] Some aspects of quantum electrodynamics of superstrong fields are considered. Physical phenomena in superstrong nuclei with Z charge greater than the critical Zcr. are discussed. For such nuclei the discrete electron spectrum level falls into low continuum. The analysis of phenomena is performed on the basis of the effective potential method. For experimental observation of phenomena taking place at Z>Zcr. one should posses nuclei with Z=170 which falls far outside the limits of the field of known nowadays stable nuclei. However electric fields of the proper value may be attained in the course of two heavy ions collision. It heavy nuclei collisions at the distances less than of a certain critical one the discrete electron level passes into the low continuum and a spontaneous positron production occurs. It is pointed out that physical phenomena taking place at the transition of discrete levels into the low continuum follow from the analysis of exact solutions of Dirac equations in the region of superstrong fields. For the last years first experiments have been performed on observation of positrons produced on irradiation of ²³⁸U, ²⁰⁸Pb, ¹⁹⁴Au, ¹⁸¹Ta and ¹³⁹La targets by lead and uranium ion beams

[en] In systems bound by the Coulomb interaction distorted at short distances there may appear, under certain conditions, a rearrangment of atomic spectrum (or the Zel'dovich effect). Specific features of this effect are discussed for states with an arbitrary angular momentum l (both with and without the absorption). The equation is studied which connects nuclear level shifts with the low-energy scattering parameters a_l, r_l. The conditions have been found under which the rearrangement of spectrum is replaced by oscillations of atomic levels. The Coulomb renormalization of scattering lengths and that of effective ranges is discussed. Some manifestations of the Zel'dovich effect in the physics of hadronic atoms and mesomolecules are considered

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[en] A correction to the Bohr-Sommerfeld quantization rules connected with the final barrier permeability (for quasistationary states) is obtained. The analytical continuation of quantization conditions in the superbarrier region is discussed. The results obtained are illustrated using the example of a exactly solvable model, as well as for the stark effect in a strong field. 27 refs.; 3 figs

[en] Renormalization of the coefficients of the ''effective range expansion'' is considered for the short-range Coulomb problem. The exactly solvable model of the Coulomb plus short range potential is considered. Exact solutions are compared with approximations frequently used in the theory of hadronic atoms

[en] Calculation of higher orders of the perturbation theory is considered for screened Coulomb potentials. Particular cases of such potentials are the Yukawa potential, a familiar object of nuclear physics, and the funnel-shaped potential, applied to analysis of heavy quark-antiquark systems. The calculation of higher perturbational orders is reduced to recursive relations, quite appropriate for computer. The Pade approximants and a modified Pade-Borel summation method are applied for calculation of sums of diverging PT series. It is shown that in the considered problems higher orders of the PT determine the behaviour of E(g) in the region of strong coupling (Esub(g)-the energy of eigen-value)

[en] The problem on calculations of virtual and resonance levels of nuclear and atomic systems is solved. An approach to this problem based on summation of perturbation theory (PT) series is described. The results of the higher order calculation of PT for screening and Coulomb potentials are used